Question

Starting from rest, a car P travels with a uniform acceleration of 2 m/s square. Starting from rest from the same point 4 sec later, a car Q travels with an acceleration of 8 m/s square in the same direction as P. find the time required by Q to overtake P. what is distance travelled by each car?​

Answer 1

The time required by Q to overtake P is 4 seconds

The distance travelled by each car is 64 m

Explanation:

For car P

Initial velocity u = 0

Acceleration a = 2 m/s²

Q starts from rest (initial velocity = 0) with acceleration 8 m/s² after 4 seconds

Let Q overtakes P in time t

The distance travelled by P in t+4 seconds = Distance travelled by Q in t seconds

Thus, from second equation of motion

$0\times (t+4)+\frac{1}{2}\times 2(t+4)^2=0\times t+\frac{1}{2}\times 8\times t^2$

$\implies (t+4)^2=4t^2$

$\implies (t+4)^2-(2t)^2=0$

$\implies (t+4-2t)(t+4+2t)=0$

$\implies (4-t)(3t+4)=0$

Therefore, t = 4 seconds (as time can't be negative)

The distance travelled by Q

$s=0\times 4+\frac{1}{2}\times 8\times 4^2$

$\implies s=64$ m

Distance travelled by car P will be the same

Hope this answer is helpful.

Know More:

Q: Two cars A and B are at rest at same point initially. If a starts with uniform velocity of 40 metre per second and B starts in same direction with constant acceleration of 4 metre per second square ,then B will catch A after how much time ?

Click Here: https://brainly.in/question/1231455