A car, moving along a straight stretch of high- way, begins to accelerate at 0.014 m/s2. It takes the car 23.2 s to cover 1 km.
How fast was the car going when it first began to accelerate?
Answer in units of m/s.
v = Vi + a t
d = Vi t + (1/2) a t^2
so
1000 = Vi (23.2) + .007(23.2)^2
solve for Vi
To find the initial velocity of the car when it began to accelerate, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
In this case, we have:
- Final velocity (v) = ? (what we want to find)
- Initial velocity (u) = ?
- Acceleration (a) = 0.014 m/s^2
- Time (t) = 23.2 s
We know that the car covers 1 km in 23.2 s. To convert 1 km to meters, we multiply it by 1000:
1 km = 1000 m
Now, let's solve the equation. Rearranging it, we have:
u = v - at
Substituting the known values:
u = 0 - (0.014 m/s^2 * 23.2 s)
Calculating:
u = -0.3224 m/s
Since we are looking for the initial velocity, the negative sign indicates that the car was moving in the opposite direction. However, we are only interested in the magnitude of the velocity, so we take the absolute value:
|u| = |-0.3224 m/s| = 0.3224 m/s
Therefore, the car was going approximately 0.3224 m/s when it first began to accelerate.