Question

You anda friend have built a cart. Your friends pushed you on a level parking lot with constant force for five seconds. Final speed 15 m/s. You then coast 80 meters to a stop. Determine the accelerations of both parts of the trip. Also, the total travel time and total distance travelled

Answer 1

Using the Newton's laws of motion
v = u + a t
Where v is the final speed , u is the initial speed, a is the acceleration and t is the time taken
Initially the cart was at rest , then it is given a constant force for 5 s , the final speed v = 15 m/s
15 = 0 + 5 x a
a = 15 / 5 = 3m/s²
To calculate the distance traveled, we use the equation
v²   = u²  + 2 a S
Where S is the distance traveled
S = v² - u²  / 2 a
S = 15² - 0²  / (2 x 3)
S = 37.5 m
After that the cart coast 80m before stopping
For this the initial velocity, u = 15m/s , the final velocity, v = 0
Again we find the deceleration
a = (v²  - u²) / 2 d
Where d is the distance covered
a = - 15² / (2 x 80)
a = - 1.406 m/s²
Now we can find the time taken for this travel
t = (v - u) / a
t = ( 0 - 15) / - 1.406
t = 14.34 s
Thus the total distance traveled by the cart
D = 37.5 m + 80 m = 117.5 m
The total time taken
T = 5 s + 14.34 s = 19.34 s