Question

A cart travelling at 50km/ h is brought to rest in 30 seconds by applying brakes
.
Find the acceleration in m/s2​

Answer 1

Given that:

• Initial velocity = 50 km/h
• Final velocity = 0 m/s
• Time taken = 30 seconds

Don't be confused! Final velocity came as zero because the car brought to rest

To calculate:

• Acceleration

Solution:

• Acceleration = -0.46 m/s²

Using concepts:

• Acceleration formula

Using formulas:

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity and t denotes time taken.

Full solution:

~ Firstly let us convert km/h into m/s

$\longrightarrow \sf 50 \times \dfrac{5}{18} \\ \\ \longrightarrow \sf \dfrac{250}{18} \\ \\ \longrightarrow \sf 13.88 \: m/s$

~ Now let's find acceleration!

$\longrightarrow \sf a \: = \dfrac{v-u}{t} \\ \\ \longrightarrow \sf a \: = \dfrac{0-13.88}{30} \\ \\ \longrightarrow \sf a \: = \dfrac{-13.88}{30} \\ \\ \longrightarrow \sf a \: = -0.46 \: m/s^2$

Answer 2

Answer :-

• The acceleration is -0.46 m/s²

Given :-

• Initial velocity of the car = 50 km/h

• Final velocity of the car = 0 m/s [ As it comes to rest after application of brakes ]  

• Time taken = 30 seconds  

To Find :-

• Acceleration in m/s²

Solution :-

Conversion of initial velocity in m/s :-

→ 50 × 5/18  

→ 13.8 m/s  

~Now, we can find the acceleration by putting the values in the first equation of motion that is :  

                ⇒ v = u + at  

where,  

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

Finding acceleration :-

→ 0 = 13.8 + ( a × 30 )  

→ a × 30 = 0 – 13.8  

→ 30a = -13.8  

→ a = -13.8/30  

→ a = -0.46 m/s²  

Henceforth, the acceleration of the car is -0.46 m/s²