Question

is the
A motorcar of mass 1200 kg is moving along a straight line
with a uniform velocity of 90 km/h. Its velocity is slowed down
to 18 km/h in 4 s by an unbalanced external force. Calculate
the acceleration and change in momentum. Also calculate the
magnitude of the force required.
​

Answer 1

Explanation:

Please refer to the workout given above.

Answer 2

$\star{\underline{\underline{\sf\red{ Solution:-}}} }$

❏Given:

• Mass of the car (m) = 1200kg
• Initial velocity (u) = 90 km/h (25 m/s)
• Terminal velocity (v) = 18 km/h (5 m/s)
• Time period (t) = 4 seconds

❏To Find:

• Acceleration (a) = ?
• Momentum (p) = ?
• Magnitude of Force = ?

❏Solution:

➲ Acceleration (a) = ${\sf{ a = \dfrac{v-u}{t} }}$

$\\ \implies{\sf{ \dfrac{5 - 25}{4} \: ms^{-2} }} \\ \\ \implies{\sf{ -5 \:ms^{-2} }}$

Therefore,

The acceleration of the car is -5 m/s².

➲ Initial momentum of the car = (m × u)

$\implies\sf{ (1200kg) \times (25m/s)} \\ \\ \implies\sf{ 30000\:kg\:ms^{-1}}$

➲ Final momentum of the car = (m × v)

$\implies\sf{ (1200kg) \times (5m/s) } \\ \\ \implies\sf{ 6000\:kg\:ms^{-1}}$

➲ Change in Momentum,

$\implies\sf{ (6000 – 30000) } \\ \\ \implies\sf{ -24000\:kg\:ms^{-1}}$

➲ External force applied = (Mass of car × acceleration)

$\implies\sf{ (1200kg) \times (-5 m/s^2) } \\ \\ \implies\sf{ -6000\:N}$

Therefore,

The magnitude of force required to slow down the vehicle to 18 km/hour is 6000 N.