Question

9. A car travels a distance 100 m with a constant
acceleration and average velocity of 20 m s-1. The final velocity acquired by the car is 25ms^-1. find the initial velocity ​

Answer 1

Given :

▪ Distance travelled = 100m

▪ Initial velocity = 20m/s

▪ Final velocity = 25m/s

To Find :

▪ Acceleration of car.

Concept :

✴ Since, acceleration has said to be constant throughout the motion, we can easily apply third equation of kinematics to solve this question.

✴ Third equation of kinematics :

▪ v² - u² = 2as

where,

v denotes final velocity

u denotes initial velocity

a denotes acceleration

s denotes distance

Calculation :

→ v² - u² = 2as

→ (25)² - (20)² = 2a(100)

→ 625 - 400 = 200a

→ 225 = 200a

→ a = 225/200

→ a = 1.125m/s²

Answer 2

${ \underline{ \underline{ \tt{ \huge{ \green{SOLUTION }}}}}}$




${ \bold{ \purple{GIVEN }}}$




${ \sf{ \star{ \blue{ \: \: distance \: covered(S) = 100 \: m}}}} \\ \\ { \star{ \sf{ \blue{ \: \: initial \: velocity(u) = 20 \: m \: {sec}^{ - 1}}}}} \\ \\ { \star{ \sf{ \blue{ \: \: final \: velocity(v) = 25 \: m \: {sec}^{ - 1}}}}}$




${ \bold{ \purple{TO \: FIND }}}$



${ \sf{ \rightarrow{acceleration}}}$




▪ using the third equation of motion to find the acceleration.....



${ \boxed{ \boxed{ \tt{ \green{ \: {v}^{2} = {u}^{2} + 2aS \: \: }}}}} \\ \\ { \sf{where}} \\ \\ { \sf{ v = }{ \green{final \: velocity}}} \\ \\ { \sf{u = }{ \green{initial \: velocity}}} \\ \\ { \sf{a = }{ \green{acceleration}}} \\ \\ { \sf{S = }{ \green{distance \: covered}}}$




▪ Putting the above given values in the formula....



${ \pink{ \sf{ {(25m {s}^{ - 1}) }^{2} = {(20m {s}^{ - 1}) }^{2} + 2a(100m)}}}$



${ \implies{ \sf{ \pink{625 {m}^{2} {s}^{ - 2} = 400 {m}^{2} {s}^{ - 2} + 200m \times a}}}} \\ \\ { \implies{ \sf{ \pink{ a \times 200m = 625 {m}^{2} {s}^{ - 2} - 400 {m}^{2} {s}^{ - 2} }}}} \\ \\ { \implies{ \pink{ \sf{a \times 200m = 225 {m}^{2} {s}^{ - 2} }}}} \\ \\ { \implies{ \pink{ \sf{a = \frac{225 {m}^{2} {s}^{ - 2} }{200m}}}}}$



${ \implies { \boxed{ \boxed{ \sf{ \red{ \: \: a = 1.125 \: m \: {sec}^{ - 2} \: \: }}}}}}$