What formula's should 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:
a) Work (W) can be calculated using the formula:
W = F * d * cos(theta)
In this case, since the car is accelerating uniformly, we can use the formula:
W = (1/2) * m * v^2
where m is the mass of the car and v is the final velocity.
b) Power (P) is defined as the rate of doing work and can be calculated using the formula:
P = W / t
where W is the work done and t is the time interval.
Now let's solve the problems step by step:
a) First calculate the final velocity using the formula:
v = u + a * t
where u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time interval.
With the given values:
u = 0 m/s
v = 12 m/s
t = 2.16 s
Rearranging the formula, we have:
a = (v - u) / t
a = (12 - 0) / 2.16
a ≈ 5.56 m/s^2
Now substitute the values of m, v, and a into the formula for work:
W = (1/2) * m * v^2
W = (1/2) * (1.04x10^3 kg) * (12 m/s)^2
W ≈ 7478.24 J
Therefore, the work done on the car is approximately 7478.24 Joules.
b) Now that we know the work done (W) and the time interval (t), we can use the formula for power:
P = W / t
P = 7478.24 J / 2.16 s
P ≈ 3460.74 W
Therefore, the power delivered by the engine in this time interval is approximately 3460.74 Watts.