Question

A car moves with uniform velocity of 100 ms-1 for 25 s. It comes to

rest in the next 10 s with uniform deceleration. Find:
1. Deceleration 2. Total distance travelled by the car.​

Answer 1

Answer:

Given :

• A car moves with uniform velocity of 100 m/s for 25 s.

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

To find :

• deceleration
• total distance travelled by the car

Solution :

 First, let's find the distance travelled by the car in the first 25 s

 Speed = distance covered/time taken

⇒ 100 = distance/25

⇒ distance = 100 × 25

⇒ distance = 2500 m

The car comes to rest in the next 10 s.

For this 10 sec,

initial velocity, u = 100 m/s

final velocity, v = 0 m/s

time taken, t = 10 s

Acceleration is the rate of change of velocity.

⇒ a = (v - u)/t

⇒ a = (0 - 100)/10

⇒ a = -100/10

⇒ a = -10 m/s²

Therefore, the required deceleration is 10 m/s²

Distance travelled in the 10 sec can be found by using the equation,

 v² - u² = 2as

⇒ 0² - 100² = 2(-10)(s)

⇒ 0 - 10000 = -20s

⇒ 20s = 10000

⇒ s = 10000/20

⇒ s = 500 m

The total distance travelled by the car = distance travelled in the first 25 s + distance travelled in the next 10 s

 = 2500 m + 500 m

 = 3000 m

Therefore, the total distance travelled by the car is 3000 m