a car starting from rest acquired a speed of 25ms-¹ in 10sec,after which it maintain this speed for 10sec. find (a)the acceleration (b) distance traveled during acceleration (c)total distance traveled?
acceleration is (25m/s)/(10s) = 2.5 m/s^2
distance during acceleration: s = 1/2 at^2 = 125m
so, total distance is 125 + 10*25 = 375 m
To find the answers to your questions, we can use the equations of motion. We'll break down each part:
(a) Finding the acceleration:
The formula to calculate acceleration is:
acceleration (a) = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 m/s (car starting from rest)
Final velocity (v) = 25 m/s
Time (t) = 10 seconds
Substituting the values into the formula, we can calculate the acceleration:
a = (v - u) / t
= (25 - 0) / 10
= 2.5 m/s²
Therefore, the acceleration of the car is 2.5 m/s².
(b) Finding the distance traveled during acceleration:
The formula to calculate distance can be derived as:
distance (s) = (initial velocity * time) + (0.5 * acceleration * time²)
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2.5 m/s²
Time (t) = 10 seconds
Substituting the values into the formula, we can calculate the distance:
s = (u * t) + (0.5 * a * t²)
= (0 * 10) + (0.5 * 2.5 * 10²)
= 0 + (0.5 * 2.5 * 100)
= 125 m
Therefore, the distance traveled during acceleration is 125 meters.
(c) Finding the total distance traveled:
Since the car maintains a constant speed of 25 m/s for an additional 10 seconds after acceleration, we can calculate the distance traveled during this period using the formula:
distance (s) = speed * time
Given:
Speed (v) = 25 m/s
Time (t) = 10 seconds
Substituting the values into the formula, we can calculate the distance:
s = v * t
= 25 * 10
= 250 m
Therefore, the distance traveled during the constant speed period is 250 meters.
To get the total distance traveled, we add the distance traveled during acceleration and the distance traveled during the constant speed period:
Total distance = Distance during acceleration + Distance during constant speed
= 125 m + 250 m
= 375 m
Therefore, the total distance traveled by the car is 375 meters.