If the force
of the road on the car's wheels, pushing it forward, is a constant 3.5 kN, and the car's mass is 2 kg, then how long will the car take to go from 15 m/s to 50 m/s?
a = F/m = 3500/2 = 1750 m/s^2
t = (V-Vo)/a = (50-15)/1750 = 0.02 s.
To calculate the time it takes for the car to go from 15 m/s to 50 m/s, we can use the concept of acceleration and Newton's second law of motion.
Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:
F = m * a
Where:
F is the net force (in Newtons),
m is the mass of the object (in kilograms), and
a is the acceleration of the object (in meters per second squared).
In this case, the force pushing the car forward is given as 3.5 kN (kilonewtons) = 3500 N. The mass of the car is 2 kg.
Since the force is constant, we can rearrange Newton's second law to solve for acceleration:
a = F / m
a = 3500 N / 2 kg
a = 1750 m/s²
Now, to find the time it takes for the car to accelerate from 15 m/s to 50 m/s, we can use the equation:
v = u + at
Where:
v is the final velocity (50 m/s),
u is the initial velocity (15 m/s),
a is the acceleration (1750 m/s²), and
t is the time taken.
Rearranging the equation to solve for time:
t = (v - u) / a
t = (50 m/s - 15 m/s) / 1750 m/s²
t = 35 m/s / 1750 m/s²
t = 0.02 s
Therefore, it will take the car approximately 0.02 seconds to go from 15 m/s to 50 m/s.