a car starts from rest moves with an acceleration of 40 km/h square calculate the time required to cover a displment of 180 km also find it's final velocity
Answers
Answer:
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Required Answer :
• The final velocity of the car = 120 km/h
• The time required to cover the displacement of 180 km = 3 hours
Given :
• Initial velocity of the car = 0 km/h [As the car was initially at rest, it's velocity will be zero.]
• Acceleration of the car = 40 km/h²
• Displacement of the car = 180 km
To find :
• Time required to cover the displacement of 180 km
• Final velocity of the car
Solution :
Here, we need to find the time and final velocity of the car. So, we will use the second equation of motion to find the time required to convert the displacement of 180 km and the third equation of motion to find the final velocity of the car.
Second equation of motion :-
- s = ut + ½ at²
where,
- s denotes the distance/displacement
- u denotes the initial velocity
- a denotes the acceleration
- t denotes the time taken
we have,
- s = 180 km
- u = 0 km/h
- a = 40 km/h²
Substituting the given values :-
→ 180 = (0)(t) + ½ (40)(t)²
→ 180 = 0 + ½ × 40 × t²
→ 180 = 20 × t²
→ 180/20 = t²
→ 9 = t²
→ Taking square root on both the sides :-
→ √9 = t
→ 3 = t
Therefore, the time required to cover the displacement of 180 km = 3 hours
Third equation of motion :-
- v² - u² = 2as
where,
- v denotes the final velocity
- u denotes the initial velocity
- a denotes the acceleration
- s denotes the distance/displacement
we have,
- u = 0 km/h
- a = 40 km/h²
- s = 180 km
Substituting the given values :-
→ v² - (0)² = 2(40)(180)
→ v² = 14400
→ Taking square root on both the sides :-
→ v = √14400
→ v = 120
Therefore, the final velocity of the car = 120 km/h