Question

A car starts from rest and attains a velocity of 10 metre per second in 40

seconds .the driver applies brakes and slows down the car to 5 metre per

second in 10 seconds. Find the acceleration of the car in both the cases?​

Answer 1

✬ Acceleration = 0.25 & 0.5 m/s² ✬

Explanation:

Given: (Solving first case)

• A car starts from rest.
• Final velocity of car is 10 m/s.
• Time taken to attain final velocity is 40 s.

To Find:

• Acceleration of the car ?

Formula to be used:

• V = u + at

Solution: Here we have

• u = 0
• v = 10 m/s
• t = 40 s
• a = ?

Substituting the values on formula

$\implies{\rm }$ 10 = 0 + a × 40

$\implies{\rm }$ 10 = 40a

$\implies{\rm }$ 10/40 = a

$\implies{\rm }$ 1/4 = a

$\implies{\rm }$ 0.25 m/s² = a

So acceleration of car in first case is 0.25 m/s².

Given: (Second case)

• Final velocity is 5 m/s.
• Initial velocity is 10 m/s.
• Time given is 10 s.

To Find:

• Acceleration of the car ?

Formula to be used:

• a = v – u/t

Solution: Here we have

• u = 10 m/s
• v = 5 m/s
• t = 10 s
• a = ?

Substituting the values on formula

$\implies{\rm }$ a = 5 – 10/10

$\implies{\rm }$ a = –5/10

$\implies{\rm }$ a = –1/2

$\implies{\rm }$ a = –0.5 m/s²

So, acceleration of car in second case is –0.5 m/s².

• (You can also solve this one by using Newton's first law of motion , used in above case)

___________________

• The velocity at which motion starts is termed as initial velocity. It is denoted by u.

• The last velocity of an object after a period of time. It is denoted by v.

• v = ut + 1/2at² ( Second law of motion)

• v² = u² + 2as ( Third law of motion )

Answer 2

‹«« In 1st Case »»›

Given :-

• Initial Velocity (u) = 0 m/s ( as it is at rest)
• Final Velocity (v) = 10 m/s
• Time (t) = 40 second

To Find :-

• Acceleration = ?

Solution :-

Formula Used :-

• v = u + at

Substituting Values

⟹ 10 = 0 + a × 40

⟹ 10 = 0 + 40a

⟹ 10 - 0 = 40a

⟹ 10 = 40a

⟹ 40a = 10

⟹ a = 10/40

⟹ a =0.25

Thus, acceleration is 0.25 m/s²

‹«« In 2nd Case »»›

Given :-

• Initial Velocity (u) = 10 m/s
• Final Velocity (v) = 5 m/s
• Time (t) = 10 second

To Find :-

• Acceleration = ?

Solution :-

Formula Used :-

• v = u + at

Substituting Values

⟹ 5 = 10 + a × 10

⟹ 5 = 10 + 10a

⟹ 5 - 10 = 10a

⟹ - 5 = 10a

⟹ 10a = -5

⟹ a = -5/10

⟹ a = -1/2

⟹ a = -0.5

Thus, here acceleration is -0.5 m/s²