Question

A racing car is traveling north. It accelerates uniformly, covering a distance of 725 m in 10 s. If it has an initial velocity of 10 m/s, find its acceleration.

Answer 1

The racing car's acceleration is calculated using the kinematic equation for uniformly accelerated motion, resulting in an acceleration of 4.5 m/s².

Step-by-step explanation:

The student's question requires finding the acceleration of a racing car that accelerates uniformly. Given that the car covers a distance of 725 m in 10 seconds, starting with an initial velocity of 10 m/s, we can use the kinematic equation for uniformly accelerated motion which is:

s = ut + ½ at²

Where:

s is the distance covered

u is the initial velocity

t is the time

a is the acceleration

Substituting the given values into this equation, we get:

725 m = (10 m/s)(10 s) + ½ a(10 s)²

After doing the calculations and rearranging for a, we find that the acceleration a is 4.5 m/s².

Answer 2

The acceleration of the racing car is 12.5 m/s²

Step-by-step explanation:

To find the acceleration of the racing car, we can use the formula:

a = (vf - vi) / t

where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken. In this case, the final velocity is the velocity at the end of the 10-second interval. We can calculate it using the formula:

vf = vi + a*t

Substituting the given values:

vf = 10 m/s + a*10 s

Since the car has covered a distance of 725 m, we can use the formula:

d = vi*t + (1/2)*a*t^2

Substituting the given values:

725 = 10*10 + (1/2)*a*(10^2)

Simplifying the equation, we get:

725 = 100 + 50a

Solving for a, we find:

a = (725 - 100) / 50 = 12.5 m/s²