A racing car initially at rest, accelerates at a uniform rate of 5. 5 m/s2 for 10 s. Calculate (i) the distance covered by the racing car from start, and (ii) the final velocity in km/h.
Answers
Required Answer :
Distance covered by the racing car from start = 250 m
Final velocity of the car in km/h = 180 km/h
Given :
- Initial velocity of the racing car = 0 m/s [The initial velocity of the racing car is zero because it was initially at rest.]
- Acceleration of the racing car = 5 m/s²
- Time = 10 s
To find :
- Distance covered by the racing car from start.
- Final velocity of the car in km/h
Solution :
To find the distance covered by the racing car, we will use the second equation of motion.
Second equation of motion :-
- s = ut + ½ at²
where,
- s = Distance/displacement
- u = Initial velocity
- a = Acceleration
- t = time
we have,
- u = 0 m/s
- a = 5 m/s²
- t = 10 s
Substituting the given values :-
⠀⠀⠀⇒ s = (0)(10) + ½ (5)(10)²
⠀⠀⠀⇒ s = 0 + ½ × 5 × 100
⠀⠀⠀⇒ s = ½ × 5 × 100
⠀⠀⠀⇒ s = 5 × 50
⠀⠀⠀⇒ s = 250
Therefore, the distance covered by the racing car from start = 250 m
Now, by using the first equation of motion we will calculate the final velocity of the racing car.
First equation of motion :-
- v = u + at
where,
- v = Final velocity
- u = Initial velocity
- a = Acceleration
- t = Time
we have,
- u = 0 m/s
- a = 5 m/s²
- t = 10 s
Substituting the given values :-
⠀⠀⠀⇒ v = 0 + (5)(10)
⠀⠀⠀⇒ v = 50
Therefore, the final velocity of the racing car (in m/s) = 50 m/s
To convert the value of final velocity from m/s into km/h, multiply is by 18/5.
⠀⠀⠀⇒ Final velocity = 50 × 18/5
⠀⠀⠀⇒ Final velocity = 10 × 18
⠀⠀⠀⇒ Final velocity = 180
Therefore, the final velocity of the racing car = 180 km/h