Question

4. A truck and a car uniformly accelerate from rest to a velocity of 3.0 m/s in equal time intervals. The truck is ten time as massive as the car. Which of the following statement is correct

(a) The acceleration of the truck is 1/10 that of the car

(b) The truck travels 1/10 the distance of the car.

(c) The force on the truck is 10 times the force on the car.

(d) all of above​

Answer 1

AnswEr :

The correct option is :

(c) The force on truck is 10 times the force on the car.

GivEn :

• A truck and a car uniformly accelerates from rest to a velocity of 3m/s in equal intervals of time .
• The mass of the truck is 10 times as massive as car

Task :

• To determine which among the following statements is correct .

Concept to be used :

Kinematics :

Equations of motion :

$\sf a = \dfrac{v-u}{t}$

Newton's second law's expression :

$\sf F = ma$

Where F is force

m is the mass of the body

a is the acceleration

SoluTion :

Given , both truck and car were at rest .

Also both has acquired same velocity , v = 3m/s in equal intervals at uniform acceleration

Therefore , acceleration of both the bodies will also be same

$\sf a = \dfrac{3-0}{t} \\\\ \sf \implies a = \dfrac{3}{t}$

But the force of both the bodies will be different because both has different masses .

Since , the truck was 10times the mass of car

So if car has mass ‘m’ , the mass of truck is ‘10m’

Force on car ,

$\sf F_{c} = m \times \dfrac{3}{t} \\\\ \sf \implies F_{c} =\dfrac{3m}{t}$

Force on truck ,

$\sf F_{t} =10m\times \dfrac{3}{t} \\\\ \sf \implies F_{t} = \dfrac{30m}{t}$

Thus ,

$\sf F_{t} = 10 F_{c}$