Question

A car, moving along a straight stretch of highway, begins to accelerate at 0.0113 m/s². It takes the car 37.3 s to cover 1 km. How fast was the car going when it first began to accelerate? Answer in units of m/s.

Answer 1

The initial velocity of the car when it began to accelerate was approximately 24.30 m/s. This was calculated using the equations of motion for uniformly accelerated motion and the given acceleration time, and distance covered.

Step-by-step explanation:

To solve for the initial speed of the car, we can use the kinematic equation for uniformly accelerated motion, which is:

v = u + at

Where:

• v is the final velocity (unknown in this case)
• u is the initial velocity (what we are trying to find)
• a is the acceleration (0.0113 m/s², given)
• t is the time (37.3 s, given)

We also know that the car covers 1 km (which is 1000 m) in 37.3 seconds. This can be expressed using the equation for distance under constant acceleration:

s = ut + ½at²

Substituting the known values:

1000 m = u(37.3 s) + ½(0.0113 m/s²)(37.3 s)²

Solving for u, we get:

u = (1000 m - ½(0.0113 m/s²)(37.3 s)²) / (37.3 s)

After solving this equation, we find that the initial velocity u is approximately 24.30 m/s.