The maker of an automobile advertises that it takes 10 seconds to accelerate from 30 kilometers per hour to 90 kilometers per hour. Assuming constant acceleration, compute the following.
(a) The acceleration in meters per second per second (Round your answer to three decimal places.)
in m/sec2
(b) The distance the car travels during the 10 seconds (Round your answer to two decimal places.)
see related questions below.
To solve this problem, we can use the formulas of motion under constant acceleration.
(a) To find the acceleration in meters per second squared (m/sec^2), we can use the equation:
acceleration = (final velocity - initial velocity) / time
Given:
initial velocity (u) = 30 kilometers per hour
final velocity (v) = 90 kilometers per hour
time (t) = 10 seconds
First, let's convert the initial and final velocities to meters per second:
u = 30 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 8.333 m/s
v = 90 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 25 m/s
Now we can plug these values into the formula to compute the acceleration:
acceleration = (v - u) / t
acceleration = (25 m/s - 8.333 m/s) / 10 s
acceleration = 16.667 m/s / 10 s
acceleration = 1.667 m/s^2 (rounded to three decimal places)
Therefore, the acceleration of the car is approximately 1.667 m/sec^2.
(b) To find the distance traveled by the car during the 10 seconds, we can use the formula:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Plugging in the values:
distance = (8.333 m/s * 10 s) + (1/2 * 1.667 m/s^2 * (10 s)^2)
distance = 83.33 m + 83.35 m
distance = 166.67 m (rounded to two decimal places)
Therefore, the car travels approximately 166.67 meters during the 10 seconds.