Question

Starting from a stationary position , a car attains a velocity of 7 m/s in 10 sec. Then, the driver of the car applies a brake such that the velocity if the car comes down to 4 m/s in the next 6 sec. Calculate the acceleration of the car in both the cases.

Answer 1

Explanation:

In 1st case,

Initial velocity (u) = 0 m/s

Final velocity (v) = 7 m/s

So,

Acceleration = $\frac{change\: in\: velocity } {time}$

= $\frac{v-u} {t}$

= $\frac{7-0} {10}$

= $\frac{7} {10} \: m/s^{2}$

= $0.7 \: m/{s}^{2}$

In 2nd case,

Initial velocity (u) = 7 m/s

Final velocity (v) = 4 m/s

So,

Acceleration = $\frac{change \:in\: velocity } {time}$

= $\frac{v-u} {t}$

= $\frac{4-7} {10}$

= $\frac{-3} {10} \:m/s^{2}$

= $-0.3 \:m/{s}^{2}$

Answer 2

Question:-

Starting from a stationary position, a car attains a velocity of 7 m/s in 10 sec. Then, the driver of the car applies a brake such that the velocity if the car comes down to 4 m/s in the next 6 sec. Calculate the acceleration of the car in both the cases.

Formula:-

${ \dashrightarrow{ \bf{ \huge{ \red{a} = { \frac{v - u}{t} }}}}}$

where,

--» a = acceleration

--» v = final velocity

--» u = initial velocity

--» t = time taken by object ( body )

Solution:-

{According to question}

• case 1 :- Starting from a stationary position, a car attains a velocity of 7 m/s in 10 sec.

Hence,

• u = 0 m/s
• v = 7 m/s
• t = 10 sec

${ \dashrightarrow{ \bf{ \red{a} = { \frac{v - u}{t} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { \frac{7 - 0}{10} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { \frac{7}{10} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { 0.7 \:m/s² }}}}$

Now, for

• Case 2 :- The driver of the car applies a brake such that the velocity if the car comes down to 4 m/s in the next 6 sec.

{ According to case 1 & from question }

Here,

• u = 7 m/s
• v = 4 m/s
• t = 6 sec

${ \dashrightarrow{ \bf{ \red{a} = { \frac{v - u}{t} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { \frac{4 - 7}{6} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { \frac{ - 3}{6} }}}}$

${ \dashrightarrow{ \bf{ \red{a} = { - 0.5 \: m/s²}}}}$

Hence in case 1 acceleration is 0.7 m/s² and in case 2 acceleration is -0.5 m/s².