What formula's do I use to solve these problems?
A 1.04x10^3 kg car accelerates uniformly from rest to 12 m/s in 2.16 seconds.
a) What is the work done on the car in this time interval? Answer in Joules.
b) What is the power delivered by the engine in this time interval? Answer in units of W
To solve these problems, you can use the following formulas from physics:
a) Work (W) = Force (F) x Distance (d) x cos(θ)
In this case, since the car is accelerating uniformly, you can use the formula:
Work (W) = (1/2) x Mass (m) x Velocity^2 (v^2)
b) Power (P) = Work (W) / Time (t)
Alternatively, you can use the formula:
Power (P) = Force (F) x Velocity (v)
Since the car is accelerating uniformly, you can use the formula:
Power (P) = (1/2) x Mass (m) x Velocity^2 (v^2) / Time (t)
Now, let's solve the problems using these formulas:
a) To find the work done on the car, we need to calculate the change in kinetic energy.
First, calculate the final kinetic energy:
Kinetic energy (K.E.) = (1/2) x Mass (m) x Final velocity^2 (v^2)
= (1/2) x 1.04x10^3 kg x (12 m/s)^2
Next, calculate the initial kinetic energy (since the car starts from rest, the initial kinetic energy is zero):
Initial kinetic energy (K.E.) = 0
The work done on the car is equal to the change in kinetic energy:
Work (W) = Final K.E. - Initial K.E.
= (1/2) x 1.04x10^3 kg x (12 m/s)^2 - 0
b) To find the power delivered by the engine, we can use either of the power formulas mentioned earlier. Let's use the second formula:
Power (P) = (1/2) x Mass (m) x Velocity^2 (v^2) / Time (t)
= (1/2) x 1.04x10^3 kg x (12 m/s)^2 / 2.16 s
To find the answer in units of Watts, divide the result by 1 (since 1 Watt = 1 Joule/second).
Therefore, the answers to the given problems are:
a) The work done on the car in this time interval is given by the formula as calculated above.
b) The power delivered by the engine in this time interval is given by the formula as calculated above, and the answer should be divided by 1 to have it in units of W.