Final answer:
To determine the distance covered by a car accelerating uniformly from rest to 120 km/h in 10 seconds, we calculate the acceleration and then use uniformly accelerated motion formulas. After converting velocity to m/s and plugging in values, we find the car covers 166.5 meters.
Step-by-step explanation:
To calculate the distance covered by a car that accelerates uniformly from rest, we will use the formula for uniformly accelerated motion:
x = x0 + v0t + ½ at2
Where:
- x is the final position or the distance covered
- x0 is the initial position, which is zero if starting from rest
- v0 is the initial velocity, which is also zero if starting from rest
- a is the acceleration
- t is the time for which the car has been accelerating
First, we need to find the acceleration (a) using the formula:
a = ∆v / t
Given that the final velocity (v) is 120 km/h (which needs to be converted to meters per second by multiplying by 1000/3600), and the initial velocity (v0) is 0 since the car is starting from rest, and the time (t) is 10 seconds:
a = (120 × 1000/3600) m/s / 10 s = 3.33 m/s2
Now, plug the acceleration and time into the distance formula:
x = 0 + 0 × 10 s + ½ × 3.33 m/s2 × (10 s)2
x = ½ × 3.33 m/s2 × 100 s2 = 166.5 meters
Thus, the car covers a distance of 166.5 meters in 10 seconds.