NCERT Solutions for Class 9 Science Chapter 9
Force and Laws of Motion
NCERT Books for Session 2022-2023
CBSE Board and UP Board
Exercises Questions
Page No-128
Questions No-5
A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes (Hint: 1 metric tonne = 1000 kg.)
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Initial velocity of the truck, u = 0 m/s
Time taken, t = 20 s
Distance covered by the stone, s = 400 m
According to the second equation of motion:
𝑠 = 𝑢𝑡 +1/2 𝑎𝑡²
We have
400 = 0 × 20 + 1/2× 𝑎 × (20)²
⇒ 400 = 200𝑎
⇒ 𝑎 = 2 𝑚/𝑠 ²
Now, Force = mass × acceleration
⇒ 𝐹 = 7000 × 2 = 14000 𝑁
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– Distance traveled by the truck (s) = 400 m
– Time taken (t) = 20 s
– Mass of the truck (m) = 7 metric tonnes = 7,000 kg (as 1 metric tonne = 1000 kg)
Calculating Acceleration:
We’ll use the kinematic equation ( s = ut + 1/2 at²), where (u) is the initial velocity (which is 0 m/s as the truck starts from rest).
s = ut + 1/2 at²
400 = 0 x 20 + 1/2 x a x 20²
400 = 200a
a = 400/200
a = 2m/s²
Calculating Force:
Now, using Newton’s second law of motion F = ma :
Given:
– Mass m = 7000 kg
– Acceleration (a) = 2 m/s²
F = ma
F = 7000 x 2
F = 14,000 N
Conclusion:
The acceleration of the truck rolling down the hill is 2 m/s² , and the force acting on it, considering its mass of 7 metric tonnes, is 14,000 Newtons.