Question

An automobile manufacturer claims that its product will, starting from rest, travel 0.40 km in 9.0 s. What is the magnitude of the constant acceleration (in m/s²) required to do this? Select one:

a. 6.6
b. 8.9
c. 4.6
d. 9.9
e. 5.6

Answer 1

The constant acceleration required for an automobile to travel 0.40 km in 9.0 seconds starting from rest is 9.9 m/s².

Step-by-step explanation:

The question concerns the constant acceleration needed for an automobile to travel 0.40 km in 9.0 seconds starting from rest. We can use the kinematic equation for uniformly accelerated motion without initial velocity (v0 = 0), which is:

s = v0t + ½at2

where:

• s is the distance traveled,
• v0 is the initial velocity,
• t is the time,
• a is the acceleration.

By substituting in the known values (s = 0.40 km = 400 meters, v0 = 0 m/s, and t = 9.0 seconds), and solving for a, we can calculate the acceleration:

400 m = ½a(9.0 s)2

400 m = ½a(81.0 s2)

400 m = 40.5a

Therefore, the acceleration a is:

a = 400 m / 40.5 m/s2 = 9.9 m/s2

The constant acceleration required is 9.9 m/s2.