a car moving at 10 metre per second was uniformly accelerated until it's velocity reaches 20 metre per second.It then maintains this speed for another 20s after which the brakes were applied and the vehicle was finally brought to rest after 10 seconds
and is there a question here?
To find the acceleration of the car, we can use the formula:
acceleration (a) = (final velocity - initial velocity) / time
Let's break down the given information step by step:
1. The initial velocity of the car is 10 meters per second.
2. The final velocity of the car is 20 meters per second.
3. The time taken for the car to reach the final velocity is not mentioned, so we don't have this specific information.
Since we don't know the time it took for the car to reach the final velocity, we'll need to use another formula to find it:
final velocity (v) = initial velocity (u) + acceleration (a) * time (t)
Let's denote the time taken for the car to reach the final velocity as t1. Using this in the formula above, we have:
20 = 10 + a * t1
Simplifying the equation, we get:
a * t1 = 10
Now, the car maintains the speed of 20 meters per second for 20 seconds. Since the car is maintaining a constant speed, the acceleration is zero during this period.
Next, the brakes are applied and the car is brought to rest (velocity becomes zero) after 10 seconds. Similar to before, we can use the formula:
final velocity (v) = initial velocity (u) + acceleration (a) * time (t)
This time, the initial velocity is 20 meters per second, the final velocity is 0, and the time is 10 seconds. Denoting the acceleration during braking as a2, we have:
0 = 20 + a2 * 10
Simplifying the equation, we get:
a2 * 10 = -20
a2 = -2
Here, we consider the acceleration as negative because it is acting in the opposite direction of motion to bring the car to rest.
So, we have obtained two equations:
1) a * t1 = 10
2) a2 = -2
Now, we need to determine the value of the acceleration (a) during the initial period. Since we don't have the value of t1 or a2, we cannot directly calculate a. However, we can solve for a using the two equations we obtained.
First, let's divide equation 1 by equation 2:
(a * t1) / a2 = (10) / (-2)
t1 / a2 = -5
Rearranging equation 1, we get:
a = 10 / t1
Substituting this into our rearranged equation, we have:
(10 / t1) / a2 = -5
Simplifying the equation, we get:
t1 = (-5) * a2 / 10
t1 = (-5) * (-2) / 10
t1 = 1
Therefore, the time taken to reach the final velocity is 1 second.
Now, we can use this value of t1 to find the acceleration (a):
a = 10 / t1
a = 10 / 1
a = 10 m/s^2
Hence, the acceleration of the car is 10 meters per second squared.