A car and a truck starts from same point along same direction ,car with initial speed 2m/s and acceleration 2 m/s^2 and truck with a constant speed 20 m/s ,find the time after which car will overtake the truck
Answers
Answer:
I think the answer is 18 sec.....
Explanation:
pls refer the attachment for steps....
The time after which the car will overtake the truck is 18 seconds.
Given: The car has an initial speed of 2 m/s and an acceleration of 2 m/s² and the truck has a constant speed of 20 m/s.
To Find: The time after which the car will overtake the truck.
Solution:
- We can solve the numerical by using the equation of motion which states that;
S = u×t + ( 1/2 )×a×t² ...(1)
Where S = distance covered, u = initial velocity, a = acceleration, t = time taken.
- Since it is said that the car and the truck start from the same point in the same direction, so we can say that the time taken by both shall be the same.
Coming to the numerical, we are given;
The constant velocity of the truck = 20 m/s
The initial velocity of the car = 2 m/s
The acceleration of the car = 2 m/s²
Let the time taken by the car to overtake the truck be 't'.
So, the distance (S) traveled by truck in this time = Speed × time
= 20t
Putting respective values in (1), we get;
S = u×t + ( 1/2 )×a×t²
⇒ 20t = 2t + ( 1/2 )×2×t²
⇒ 20t = 2t + t²
⇒ t² - 18t = 0
⇒ t ( t - 18 ) = 0
⇒ t = 0, 18
The time taken is = 18 s
Hence, the time after which the car will overtake the truck is 18 seconds.
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