Question

5 A car moves with uniform
velocity of 40 ms for 5 s. It
comes to rest in the next 10 s
with uniform deceleration. Find
(i) deceleration (ii) total
distance travelled by the car.
​

Answer 1

Answer:

deceleration = 4 m/s²

total distance travelled = 400 m

Explanation:

Given :

• A car moves with uniform  velocity of 40 m/s for 5 s.

• It  comes to rest in the next 10 s  with uniform deceleration.

To find :

• the deceleration
• the total distance travelled by the car

Solution :

The car comes to rest in the next 10 s with uniform acceleration.

here,

initial velocity, u = 40 m/s

final velocity, v = 0 m/s

time taken, t = 10

From the first equation of motion,

v = u + at

0 = 40 + a(10)

0 - 40 = 10a

10a = -40

 a = -40/10

 a = -4 m/s²

Therefore, the deceleration is 4 m/s²

Total distance travelled :

In the first 5 seconds,

distance travelled = speed × time = 40 m/s × 5 s = 200 m

In the next 10 seconds,

to find the distance travelled, we need to use the third equation of motion.

v² - u² = 2as

0² - 40² = 2(-4)(s)

-1600 = -8s

  8s = 1600

   s = 1600/8

   s = 200 m

Total distance travelled = distance travelled in first 5 seconds + distance travelled in the next 10 seconds

 = 200 m + 200 m

 = 400 m