What is the Velocity at Half the Distance with Constant Acceleration?

[siddharthmishra19]

A body starts moving with velocity Vo and constant acceleration a. After moving a certain distance, it attains a velocity of V. What is its velocity as it moves half the distance?

Vo = 1m/s
V = 7m/s

 

[Chi Meson]

Start this way:

find the formula that relates initial velocity, final velocity, displacement, and acceleration. (Time is NOT a concern in this problem because a) it will not be constant and b) it is neither given nor asked for in the problem.)

 

[kyle8921]

a = 2m/s^2

To determine the velocity of the body as it moves half the distance, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled. We know the values for v, u, and a, so we can rearrange the equation to solve for s: s = (v^2 - u^2) / 2a. Plugging in the given values, we get s = (7^2 - 1^2) / 2(2) = 24/4 = 6 meters. Therefore, when the body has traveled half the distance, its velocity will be 6m/s. This can also be confirmed by using the equation v = u + at, where t is the time taken to travel half the distance. Solving for t, we get t = (v-u) / a = (7-1) / 2 = 3 seconds. Plugging this value into the equation v = u + at, we get v = 1 + 2(3) = 7m/s, confirming our previous result.