A car starts at rest and accelerates at a constant rate for 12 seconds to a speed of 30 m/s.
a) What is the acceleration?
b) What is the total distance traveled in these 12 seconds?
a = (30m/s)/(12s) = 30/12 m/s^2
s = 1/2 at^2 = ...
12
a) To find the acceleration, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Here, the initial velocity is 0 m/s (since the car starts at rest), the final velocity is 30 m/s, and the time is 12 seconds.
acceleration = (30 m/s - 0 m/s) / 12 s
acceleration = 30 m/s / 12 s
acceleration = 2.5 m/s^2
So, the acceleration of the car is 2.5 m/s^2.
b) To find the total distance traveled in these 12 seconds, we can use the equation for displacement:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car starts at rest, the initial velocity is 0 m/s.
displacement = (0 m/s * 12 s) + (0.5 * 2.5 m/s^2 * (12 s)^2)
displacement = 0 m + 0.5 * 2.5 m/s^2 * 144 s^2
displacement = 0 m + 0.5 * 2.5 m/s^2 * 144 s^2
displacement = 0 m + 180 m
displacement = 180 m
So, the total distance traveled by the car in these 12 seconds is 180 meters.
To find the answers to these questions, we can use the equations of linear motion. The two key equations that we will use are:
1) v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
2) s = ut + (1/2)at^2, where s is the distance traveled.
a) To find the acceleration, we can use the first equation. We know that the car starts at rest, so the initial velocity u is 0 m/s. The final velocity v is given as 30 m/s, and the time t is given as 12 seconds. Plugging these values into the equation, we get:
30 = 0 + a(12)
30 = 12a
To find a, we divide both sides of the equation by 12:
a = 30/12
a = 2.5 m/s^2
Therefore, the acceleration of the car is 2.5 m/s^2.
b) To find the total distance traveled in 12 seconds, we can use the second equation. Again, the initial velocity u is 0 m/s, and the time t is 12 seconds. We need to find the distance s. Plugging these values into the equation, we get:
s = 0(12) + (1/2)(2.5)(12)^2
s = 0 + (1/2)(2.5)(144)
s = (1/2)(2.5)(144)
s = 180 meters
Therefore, the total distance traveled by the car in these 12 seconds is 180 meters.