A racing car, initially at rest, picks up a velocity of 180 km h-1 in 5 s. Calculate :
(i) final velocity in m s-1
(ii) average velocity
(iii) acceleration (iv) distance covered by the car.
Answers
Given :-
- Initial velocity, u = 0 m/s (as it is at rest)
- Final velocity, v = 180 km/h
- Time, t = 5 seconds
To find :
- Final velocity in m/s
- Average speed
- Acceleration
- Distance covered by the car
According to the question,
i)
➞ 180 km/h into m/s
➞ 180 × 1000 ÷ 3600
➞ 50 m/s
So,the final velocity is 50 m/s.
ii)
➞ Average velocity = Final velocity + Initial velocity ÷ 2
➞ Average velocity = 50 + 0 ÷ 2
➞ Average velocity = 25
So,the average velocity is 25 m/s.
iii)
➞ v = u + at
Where,
- v = Final velocity
- u = Initial velocity
- a = Acceleration
- t = Time
➞ 50 = 0 + a × 5
➞ 50 - 0 = 5a
➞ 50 = 5a
➞ 50 ÷ 5 = a
➞ 10 = a
So,the acceleration is 10 m/s².
iv)
➞ s = ut + ½ at²
Where,
- s = Distance
- u = Initial velocity
- a = Acceleration
- t = Time
➞ s = 0 × 5 + ½ × 10 × 5 × 5
➞ s = 0 + 5 × 25
➞ s = 0 + 125
➞ s = 125
So,the distance covered by the car is 125 metres.
Answer:
Given :-
- A racing car, initially at rest, picks up a velocity of 180 km/h in 5 seconds.
To Find :-
- Final velocity in m/s
- Average velocity
- Acceleration
- Distance covered by the car.
Solution :-
❶ To find final velocity in m/s
⇒ 180 km/h
⇒ 180 × 5/18 m/s
➠ 50 m/s
∴ The final velocity in m/s is 50 m/s .
❷ To find average velocity we know that,
✪ Average Velocity = Initial velocity + Final velocity ÷ 2 ✪
↬ Average Velocity = 0 + 50 ÷ 2
↬ Average Velocity = 50 ÷ 2
➡ Average velocity = 25 m/s
∴ The average velocity of car is 25 m/s .
❷ To find acceleration, we know that,
✦ v = u + at ✦
↦ 50 = 0 + a(5)
↦ 50 = 5a
↦ 50 ÷ 5 = a
↦ 10 = a
➥ a = 10 m/s²
∴ The acceleration of a car is 10 m/s² .
❹ To find distance covered by the car we know that,
❖ s = ut + ½ at² ❖
➟ s = (0)(5) + ½ × (10)(5)²
➟ s = 0 + ½ + 10 × 25
➟ s = 0 + 5 × 25
➟ s = 5 × 25
➽ s = 125 m
∴ The distance covered by a car is 125 m .