Question

Two cars A and B are moving on parallel roads in the same direction. Car A moves with constant velocity 30m/s and car B moves with constant acceleration 2.5m/s² . At , car A is ahead of car B and car B is moving with 12m/s velocity . The distance travelled by car B until it overtakes car A is __________.

Answer 1

The question involves solving for the distance at which car B overtakes car A, requiring the use of kinematic equations for displacement with constant velocity and constant acceleration.

Step-by-step explanation:

The question asks to calculate the distance traveled by car B until it overtakes car A, where car A is moving with a constant velocity of 30 m/s and car B starts with an initial velocity of 12 m/s and has a constant acceleration of 2.5 m/s².

To solve this, we can equate the displacement (s) of car A with the displacement of car B as they will be at the same position when car B overtakes car A.

For car A, moving with constant velocity (v), the displacement after time t is:

sA = vA × t

For car B, starting with an initial velocity (u) and accelerating at a constant rate (a), the displacement using the kinematic equation is:

sB = uB × t + ½ a × t²

We'll solve these two equations by setting sA equal to sB and solve for t. Then plug the value of t back into one of the displacement equations to find the distance.