Question

A soccer player runs across a soccer field. a. If the soccer player runs with a speed of 4.6 m/s, how long does it take him to run 60 m? b. It takes the soccer player 3 seconds to reduce his speed to 3.1 m/s. What is his acceleration? c. The soccer player is running at a speed of 4 m/s when he slides on the ground, coming to a stop in a distance of 2 m. What was his acceleration? d. The soccer player accelerates from rest at a rate of 3.1 m/s2. How far does he run in 1.5 seconds? Physics

Answer 1

A. speed= distance/ time
s= 4.6m/s
d=60m
4.6= 60/t
4.6t= 60
t= 13.04 seconds

b. acceleration= (the change in velocity/speed)/(time) this is the same as a=Δv/t
a= unkown
Δv= (final speed - initial speed) =  3.1m/s - 4.6m/s=  -1.5m/s
t=3 seconds

a=Δv/t= -1.5/3= -0.5m/s²
answer: the soccer player decelerated by 0.5m/s². This means his speed is decreasing by 0.5m/s². We know it is decreasing because the answer is negative.

c. list given information:
final velocity/speed(FS)= 0m/s
initial velocity/speed(IS)= 4m/s
distance(d)= 2m
time(t)= UNKOWN
acceleration(a)= UNKOWN
(side note: velocity and speed are almost the same thing. The difference between the two words is that velocity usually has a direction and can be negative. Speed cannot be negative. If your problems use the word "speed" I would recommend you continue to use the word "speed" as well. I wanted to clarify this so that you didn't think I was saying to divide velocity by speed.)

Equation: (final speed²)= (inital speed²)+ 2(distance)(acceleration)
FS²=IS²+2da
(0²)= (4²)+ 2(2)a
0=16+4a
-4a=16
a= -4m/s²
answer: The deceleration(decreasing acceleration) is 4m/s². This is because the speed was changing at a rate of negative 4 meters per second squared until reaching a final speed of 0m/s.

d. List given information:
Initial speed: 0m/s (we know he started from "rest" which means his IS was 0) 
Final speed: UNKNOWN 
time= 1.5seconds
distance= UNKOWN
acceleration= 3.1m/s²


Equation: distance= (initial speed * t) + ((1/2)*(acceleration)*(time²)
d= (IS)t + (1/2)at²
d= (0)(1.5)+ (1/2)(3.1)(1.5²)
d= 0 + 3.4785
d≈3.5 meters

Any confusion or questions? Hope this helped!