A certain car is capable of accelerating at a
uniform rate of 0.84 m/s
2
.
What is the magnitude of the car’s displacement as it accelerates uniformly from a speed
of 84 km/h to one of 97 km/h?
Answer in units of m
vf^2=vi^2+2ad solve for d
change all velocities to m/s before computing.
To find the magnitude of the car's displacement, we can use the equations of motion.
The first step is to convert the initial and final speeds from km/h to m/s since the acceleration is given in m/s².
Initial speed = 84 km/h = (84 * 1000) / 3600 m/s = 23.33 m/s
Final speed = 97 km/h = (97 * 1000) / 3600 m/s = 26.94 m/s
Next, we need to find the time it takes for the car to change its speed. We can use the equation:
vf = vi + at
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Rearranging the equation to solve for time (t), we get:
t = (vf - vi) / a
t = (26.94 - 23.33) / 0.84 = 4.32 s
Now, we can use the equation for displacement to find the magnitude:
s = vi * t + (1/2) * a * t²
s = 23.33 * 4.32 + (1/2) * 0.84 * (4.32)^2
s = 100.7536 + 8.05376
s = 108.80736 m
Therefore, the magnitude of the car's displacement as it accelerates uniformly from a speed of 84 km/h to one of 97 km/h is approximately 108.81 m.