Question

A car starts from rest and attains a velocity of 54 km/h in 2 mins. The driver applies brakes and decelerates the car to 36 km/h in 10 sec. Find the acceleration of the car in both the cases.

Answer 1

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

★★★★ Case 1 ★★★★

★ Given :

Initial Velocity of car (u) = 0 km/h = 0 m/s

Final velocity of car (v) = 54 km/h * 5/18 = 15 m/s

Time taken (t) = 2 mins = 120 s

__________________________

★ To Find :

We have to find the acceleration in both cases

__________________________

★ Solution :

We know the formula to find the value of acceleration

$\Large{\implies{\boxed{\boxed{\sf{a = \frac{v - u}{t}}}}}}$

_______________[Put Values]

$\sf{→ a = \frac{15 - 0}{120}} \\ \\ \sf{→ a = \frac{\cancel{15}}{\cancel{120}}} \\ \\ \sf{→ a = \frac{1}{8}} \\ \\ \sf{→ a = 0.125} \\ \\ \Large{\implies{\boxed{\boxed{\sf{a = 0.125 \: ms^{-2}}}}}}$

$\rule{200}{2}$

★★★★ Case 2 ★★★★

★ Given :

Initial Velocity of car (u) = 54 km/h = 15 m/s

Final velocity of car (v) = 36 km/s * 5/18 = 10 m/s

Time taken (t) = 2 mins = 10 s

__________________________

★ To Find :

We have to find the acceleration in both cases

__________________________

★ Solution :

We know the formula to find the value of acceleration

$\Large{\implies{\boxed{\boxed{\sf{a = \frac{v - u}{t}}}}}}$

_______________[Put Values]

$\sf{→ a = \frac{10 - 15}{10}} \\ \\ \sf{→ a = \frac{\cancel{-5}}{\cancel{10}}} \\ \\ \sf{→ a = \frac{-1}{2}} \\ \\ \sf{→ a = -0.5} \\ \\ \Large{\implies{\boxed{\boxed{\sf{a = -0.5 \: ms^{-2}}}}}}$

-ve sign denotes that the negative acceleration.

Answer 2

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

• Acceleration in 1st Case is 0.125 m/s²
• Acceleration in 2nd case is -0.5 m/s²

$\rule{200}{0.5}$

$\underline{\underline{\mathfrak{Step-By-Step-Explanation :}}}$

➠ 1st Case :

Given :

• Initial velocity (u) = 0 m/s
• Final velocity (v) = 54 km/h = 15 m/s
• Time (t) = 2 mins = 2*6 = 120s

______________________

To Find :

• Acceleration

_______________________

Solution :

Use formula for acceleration :

$\large{\boxed{\sf{a \: = \: \dfrac{v \: - \: u}{t}}}} \\ \\ \implies {\sf{a \: = \: \dfrac{15 \: - \: 0}{120}}} \\ \\ \implies {\sf{a \: = \: \dfrac{15}{120}}} \\ \\ \implies {\sf{a \: = \: 0.125}} \\ \\ \underline{\sf{\therefore \: Acceleration \: is \: 0.125 \: ms^{-2}}}$

$\rule{200}{2}$

➠ 2nd Case :

• Final velocity (v) = 36 km/h = 10
• Initial velocity (u) = 15 m/s
• Time (t) = 10s

Use formula for acceleration :

$\large{\boxed{\sf{a \: = \: \dfrac{v \: - u}{t}}}} \\ \\ \implies {\sf{a \: = \: \dfrac{10 \: - \: 15}{10}}} \\ \\ \implies {\sf{a \: = \: \dfrac{-5}{10}}} \\ \\ \implies {\sf{a \: = \: -0.5}} \\ \\ \underline{\sf{\therefore \: Acceleration \: is \: -0.5 \: ms^{-2}}}$