Question

A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 seconds. Find it's acceleration. Find the force acting on it if it's mass is 7 metric tonnes. *​

Answer 1

Answer:

$\bigstar{\bold{Acceleration=2\:m/s^{2} }}$

$\bigstar{\bold{Force=14000\:N}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Initial velocity (u) = 0 m/s
• Distance travelled (s) = 400 m
• Time taken (t) = 20 s
• Mass = 7 metric tonnes = 7000 kg

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Acceleration(a)
• Force acting on it (F)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the acceleration of the truck

→ By the second equation of motion,

  s = ut + 1/2 a t²

→ Substituting the datas we get,

  400 = 0 × 20 + 1/2 × a × 20 × 20

  400 = 200 a

  a = 400/200

  a = 2 m/s²

→ Hence acceleration of the truck is 2 m/s²

$\boxed{\bold{Acceleration=2\:m/s^{2} }}$

→ Now by Newton's second law of motion, we know that

  F =  m a

→ Substituting the datas we get,

  F = 7000 × 2

  F = 14000 N

→ Hence the force acting o the truck is 14000 N

$\boxed{\bold{Force=14000\:N}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The three equations of motion are:

• v = u + at
• s = ut + 1/2 at²
• v² - u² = 2as

Answer 2

Given :

• Initial velocity (u) = 0 m/s
• Time (t) = 20 seconds
• Distance (s) = 400 m
• Mass (m) = 7 metric tonnes

To find :

• Acceleration
• Force acting on it

According to the question,

By using Newton's second equation of motion we will calculate acceleration,

$\star \: \boxed {\mathsf \red{s = ut + \frac{1}{2} {at}^{2} }}$

$\implies\sf{400 = 0 \times 20 + \frac{1}{2} \times a \times ( {20)}^{2} }$

$\implies \sf{400 = 0 + \frac{1}{2} \times a \times 400 }$

$\implies \sf{400 =a \times 200}$

$\implies \sf{a = \cancel\frac{400}{200} {}^{ \: \: 2} }$

$\implies \sf{a = 2 \: {ms}^{ 2} } \green\bigstar$

So,the acceleration is 2 m/s²..

Now we will calculate the force applied,

$\star \boxed{ \sf \red{F = ma}}$

°.° 1 metric tonnes = 1000 kg

.°. 7 metric tonnes = 7 × 1000

$\implies\sf{7 \times 1000 \times 2}$

$\implies \sf{14000 \: N} \green \bigstar$

So,the force is 14000 N..

_________....

Here,

• N stands for Newton
• F stands for Force
• m stands for Mass
• a stands for Acceleration
• u stand for Initial velocity
• t stands for Time