Question

A car of mass 500 kg is starts from rest. and
is acted upon by a forward force of 200 N due
to engine and retarding force of 50 N.
Calculate the velocity after 5 seconds.​

Answer 1

Given :

• Mass of Car (m) = 500 kg
• Initial velocity (u) = 0 m/s
• Forward Force acting (F1) = 200 N
• Retarding Force (F2) = - 50 N
• Time interval (t) = 5 seconds

To Find :

• Velocity of the car

Solution :

We're given that the forward force is 200 N and retarding force is 50 N. We've to take sign of retarding force as negative because it is in opposite direction of motion. So, equivalent force will be :

$\implies \sf{F_{eq} \: = \: F_1 \: + \: F_2} \\ \\ \implies \sf{F_{eq} \: = \: 200 \: + \: (-50)} \\ \\ \implies \sf{F_{eq} \: = \: 200 \: - \: 50} \\ \\ \implies \sf{F_{eq} \: = \: 150}$

$\therefore$ Equivalent force is 150 N

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Now, we've to find acceleration of the car.

$\implies \sf{F \: = \: ma} \\ \\ \implies \sf{150 \: = \: 500a} \\ \\ \implies \sf{a \: = \: \dfrac{150}{500}} \\ \\ \implies \sf{a \: = \: 0.3}$

$\therefore$ Acceleration of the car is 0.3 m/s²

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Now, we've to find final velocity

$\implies \sf{v \: = \: u \: + \: at} \\ \\ \implies \sf{v \: = \: 0 \: + \: 0.3 \: \times \: 5} \\ \\ \implies \sf{v \: = \: 0 \: + \: 1.5} \\ \\ \implies \sf{v \: = \: 1.5}$

$\therefore$ Velocity of car when time is 5 seconds is 1.5 m/s

Answer 2

Given :

• Velocity of car (V1) = 0 m/s
• Mass of car (m) = 500 kg
• Forward force (F1) = 200 N
• Retarding force (F2) = 50 N
• Time taken (t) = 5 seconds

To Find :

We have to Calculate the velocity after 5 seconds.​

Explanation :

$\sf{\dashrightarrow Equivalent \: Force = F_1 - F_2} \\ \\ \sf{\dashrightarrow Force = 200 - 50} \\ \\ \sf{\dashrightarrow Equivalent \: Force = 150 \: N} \\ \\ \large{\implies{\boxed{\boxed{\boxed{\sf{Equivalent \: Force = 150 \: N}}}}}$

$\rule{200}{2}$

$\large{\implies{\boxed{\boxed{\boxed{\sf{Force = Mass \times Acceleration}}}}}$

$\sf{\dashrightarrow Force = Mass \times \bigg( \dfrac{V_2 - V_1}{t}} \\ \\ \sf{\dashrightarrow 150 = 500 \times \bigg( \dfrac{V_2 - 0}{5}} \\ \\ \sf{\dashrightarrow \dfrac{150 \times 5}{500} = V_2} \\ \\ \sf{\dashrightarrow V_2 = 1.5} \\ \\ \large{\implies{\boxed{\boxed{\boxed{\sf{V_2 = 1.5 \: ms^{-1}}}}}}$