Math and Arithmetic

Physics

Kinematics

The gradient of the tangent to the graph at the instant in question.

The tangent at a point on the position-time graph represents the instantaneous velocity. 1. The tangent is the instantaneous slope. 2. Rather than "average" velocity, the slope gives you "instantaneous" velocity. The average of the instantaneous gives you average velocity.

The average acceleration can be obtained by finding the slope of the graph. The instantaneous acceleration is found by drawing a tangent to a particular point on the graph (instant) and finding the slope of than tangent.

By getting the displacements S1 at time t1 and S2 at time t2, now we use the expression S2 - S1 / t2 - t1. This gives the average velocity in the duration of time from t1 to t2. Instantaneous velocity is got by finding the slope of the tangent drawn to the curve at that instant of time.

The Sun's gravity and the Earth's velocity (at a tangent to its orbit, at any instant) around the Sun.

As an object goes round in a circular path, then its velocity will along the tangent at that instant. But centripetal acceleration is normal to that tangent and so along the radius of curvature. As acceleration is perpendicular to the velocity, the direction aspect is ever changing and so the object goes round the circular path.

Instantaneous acceleration... Slope of the tangent to a velocity time graph at any point is of the form velocity/time=acceleration.

Just by drawing a tangent to the curve at a given point and finding its slope we can find the acceleration at that instant.

a=dv/dt=d/dt(dx/dt)=d^2x/dt^2Is the rate of a tangent to the slope of a graph signifying velocity versus time. It is a snapshot of acceleration at a precise moment in time based on the relative changes in velocity over time. It is the limit of acceleration for any given point within the displacement vector.Instantaneous acceleration is how fast a velocity is changing at a specific instant.

The tangent (of a curve) is a vector that is tangent (perpendicular to the normal), i.e. the instantaneous velocity of the curve at a specific point. As such, the initial tangent is the initial velocity of the curve at the point where t=0. Stated in other terms, the tangent is the slope of the line at a point. This is expressed (in two dimensions, but applicable to higher dimensions), as the line that has x and y coordinates equal to the point of tangency, and slope equal to the limit of delta y over delta x as delta x (and delta y) approaches zero.

It is called instantaneous velocity and is the slope of the line tangent to the point on the position versus time graph. It also can be found by differentiating position with respect to time (i.e. dx/dt)Instantaneous Speed

x axis = time, y axis = distance since magnitude of velocity (speed) = distance / time the gradient of a tangent of the line at any point represents instant magnitude of velocity (speed).

The Instantaneous rate, or the rate of decomposition at a specific time, can be determined by finding the slope of a straight line tangent to the curver at that instant.

Instantaneous acceleration.

No. What you've described is instantaneous acceleration. To lift the average speed from a graph, you need a graph of distance-time. Pick two points in time, and find the distance at both those times. The average speed over that time interval is (difference between the distances at the beginning and end) divided by (difference between the two times). If you're just going for the average, then it doesn't matter what happened during the interval, only the values at the end-points. The slope of the line tangent to the curve on your distance-time graph is the instantaneous speed at that point in time. We're saying "speed" in this discussion because there's actually no such thing as a graph of velocity. No simple thing anyway. Velocity is a vector, whose magnitude is speed and which includes a direction. It's easy to graph speed vs time, but not that easy to graph direction vs time. So all the graph shows is speed.

Velocity is a vector; having direction. So, when changing direction constatly to have velocity a tangent can be drawn to the constantly changing path of the object having velocity.

the instantaneous rae, or the rate of decomposition at a specific time, can be determined by fining the slope of the staight line tangent to the curve at that instant.

Velocity of the Particle -PRAKHAR

The same as anywhere else. The distance covered in a short time, divided by the time, and you make that time tend to zero to give the linear speed at any instant. Strictly velocity is a vector so besides having magnitude equal to the speed it has a direction, along the tangent if the object is moving in a curve.

There is no specific name for such an angle.

Tangent is used in calculus to compute the slope of a curve. Because curves do not have uniform slopes, unlike lines, their slopes change. A tangent is the slope of a curve at a specific point.

It will measure acceleration in the direction towards or away from the origin.

Tangent of the slope at any point = velocity

The slope of the tangent line in a position vs. time graph is the velocity of an object. Velocity is the rate of change of position, and on a graph, slope is the rate of change of the function. We can use the slope to determine the velocity at any point on the graph. This works best with calculus. Take the derivative of the position function with respect to time. You can then plug in any value for x, and get the velocity of the object.

It is the instantaneous velocity, if it were a graph with velocity over time, then it would be acceloration

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