A race car has a mass of 710 kg. It starts from rest and travels 40.0 m in 3.0 s. The car is uniformly accelerated during the entire time. What net force is exerted on it?
First calculate the acceleration from the distance and time using the formula:
S=v0t+(1/2)at²
where
a=acceleration
S=distance
v0=initial velocity
t=time
a=2(S-v0t)/t² (assumed uniform)
Find force F from
F=ma
Thanks a lot! I got F = 6311.11 N.
The answer is correct!
Have a merry Christmas, and enjoy your holidays!
To find the net force exerted on the race car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Given:
Mass of the race car (m) = 710 kg
Distance traveled (d) = 40.0 m
Time taken (t) = 3.0 s
First, we need to find the acceleration of the race car using the equation:
Acceleration (a) = (change in velocity) / (time taken)
Note that the race car starts from rest, so its initial velocity (u) is 0 m/s.
Change in velocity (Δv) = (final velocity - initial velocity)
Final velocity (v) can be determined using the equation:
v = u + a * t
Since the car starts from rest, u = 0 m/s.
Substituting the given values into the equation, we have:
Δv = v - u = a * t
Δv = final velocity (v)
Δv = (d / t)
a = Δv / t
a = (d / t) / t
a = d / t^2
Now that we have the acceleration, we can calculate the net force using the equation:
Net force (F) = mass (m) * acceleration (a)
Substituting the given values, we have:
F = m * a
F = 710 kg * (d / t^2)
Plugging in the values for the distance and time, the net force exerted on the race car is:
F = 710 kg * (40.0 m / (3.0 s)^2)
Calculating this expression will give you the net force exerted on the race car.
F*X = KE increase = (1/2) M Vfinal^2
Vfinal = 2*Vaverage = 2*X/T =2*(40/3) = 26.67 m/s
F = (1/2)*(710)*(26.67)^2/40 = 6313 N
We agree