Question

A particle moving in a straight line with uniform deceleration has a velocity of 40 m/s at point P, 20 m/s at point Q and the particle finally comes to rest at point R, where QR is equal to 50 m. Calculate i. the distance PQ, ii. time taken for PQ and iii. time taken for PR.

Answer 1

To find the distance PQ, subtract the position of point Q from the position of point P. The distance PQ is 20 meters. The time taken for PQ is 2 seconds and the time taken for PR is 4 seconds since the particle comes to rest at point R.

Step-by-step explanation:

To find the distance PQ, we can subtract the position of point Q from the position of point P. Since we know the particle's velocity at both points P and Q, we can use the kinematic equation:

d = vf - vi

where d is the distance, vf is the final velocity, and vi is the initial velocity. Substituting the known values, we get:

d = 20 m/s - 40 m/s = -20 m/s

Since distance is a scalar quantity, the negative sign indicates that the particle is moving in the opposite direction from P to Q. Therefore, the distance PQ is 20 meters.

To find the time taken for PQ, we can use the kinematic equation:

d = vit + (1/2)at2

where a is the acceleration and t is the time. Rearranging the equation, we get:

t = (vf - vi)/a

Substituting the known values, we get:

t = (20 m/s - 40 m/s)/(-10 m/s2) = 2 seconds

Since the particle comes to rest at point R, we can find the time taken for PR by using the equation:

vf = vi + at

where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation and substituting the known values, we get:

t = (0 m/s - 40 m/s)/(-10 m/s2) = 4 seconds