Question

a car of mass 1000 kg develop a mass of 400N over distance of 49meters. consider car is at rest. find the final velocit and time for which its accelerates.

Answer 1

Given :-

• Mass of the car = 1000 kg
• Force = 400 N
• Distance traveled = 49 m
• Initial velocity of the car = 0 m/s (rest)

To find :-

• Acceleration
• Final velocity

How to solve :-

• As nothing is given about the acceleration of the car we can assume it to be constant
• As the acceleration is constant we can use the third equation of motion in order to solve this question
• But first we need to find the value of acceleration ,in order to do that simply apply the Newton's second law of motion

Solution :-

We know that ,

$\bigstar \boxed{\mathtt{ \pink{F = ma}}}$

here ,

• F = force
• m = mass
• a = acceleration

$\implies\mathtt{ a = \dfrac{F}{m} }$

$\implies\mathtt{ a = \dfrac{400}{1000} }$

$\implies\mathtt{ \red{a = 0.4\dfrac{m}{ {s}^{2} } }}$

The acceleration of the car is 0.4 m /s²

________________

Now let's use the third equation of motion in order to find the final velocity of the car

$\bigstar \boxed{\mathtt{ \pink{ {v}^{2} = {u}^{2} + 2as}}}$

here ,

• v = final velocity
• u = initial velocity
• a = acceleration
• s = distance

Now let's substitute the given values in the above equation ,

$\implies\mathtt{ {v}^{2} = 0 + 2 \times 0.4 \times 49 }$

$\implies\mathtt{ {v}^{2} = 98 \times 0.4 }$

$\implies\mathtt{ {v}^{2} = 39.2 }$

$\implies\mathtt{ v = \sqrt{ 39.2} }$

$\implies\mathtt{ \red{v = 6.26 \dfrac{m}{s} }}$

The final velocity of the car is 6.26 m /s