During a lawnmower race, a rider starts from rest and accelerates at 1 m/s/s for 10 seconds. The rider then maintains a constant velocity for the remainder of the race, which takes an additional 20 seconds.
A) How far was the race?
B) What was the lawnmower's average velocity for the race?
distance= 1/2 *1*10 + 1*10*20
average velocity= distance/30seconds
check my thinking.
Thanks!
To answer these questions, we need to understand the concepts of acceleration, velocity, and distance.
Acceleration is the rate at which an object's velocity changes. In this case, the rider starts from rest and accelerates at 1 m/s/s, which means the velocity increases by 1 m/s every second.
Velocity is the speed of an object in a given direction. When the rider maintains a constant velocity, it means the speed stays the same, and there is no change in direction.
Distance is defined as the total length covered by an object. In this scenario, we need to calculate the distance covered during the race.
A) To calculate the distance covered during the race, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the rider starts from rest, the initial velocity is 0 m/s. The time for the first phase of acceleration is 10 seconds, and the acceleration is 1 m/s/s. Thus, we can calculate the distance covered during the acceleration phase:
distance = (0 * 10) + (0.5 * 1 * 10^2)
distance = 0 + (0.5 * 1 * 100)
distance = 0 + 0.5 * 100
distance = 50 meters
During the second phase of the race, the rider maintains a constant velocity for 20 seconds, so the distance covered is given by:
distance = (constant velocity * time)
distance = (constant velocity * 20)
Since we don't have the constant velocity, we cannot determine the distance covered during this phase.
To calculate the total distance of the race, we add the distance covered during acceleration (50 meters) to the distance covered during the constant velocity phase:
total distance = 50 meters + distance covered during constant velocity phase
B) The average velocity for the race can be calculated using the formula:
average velocity = total distance / total time
We know that the total time of the race is 30 seconds (10 seconds of acceleration + 20 seconds of constant velocity). Using the total distance we calculated in part A (50 meters + distance covered during constant velocity phase), we can determine the average velocity for the race.