Answer:
a) The acceleration of the jogger is 1.5 m/s²
b) the acceleration of the car is also 1.5 m/s²
c) Yes, the car travels 76 m farther than the jogger.
Explanation:
a) The acceleration of an object is the variation of its velocity over time:
a = final velocity - initial velocity / time
for the jogger:
a = 3.0 m/s - 0 m/s / 2.0 s = <u>1.5 m/s ²</u>
b) For the car:
a = 41.0 m/s - 38.0 m/s / 2.0 s = <u>1.5 m/s²</u>
c) Let´s see the position of the car after 2 seconds.
The equation for the position of an accelerated object moving in a straight line is:
x = x0 + v0* t +1/2 * a * t²
Where:
x = position of the car at time "t"
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
Let´s consider x0 = 0 because the origin of the reference system is located where the car starts accelerating. Then:
x = 38,0 m/s * 2 s + 1/2 * 1.5 m/s ² * (2.0 s)²
x = 79 m
In the same way, we can calculate the position of the jogger:
x = 0 m/s * t + 1/2 * 1.5 m/s ² * (2.0 s)²
x = 3 m
<u>The car travels 79 m - 3 m = 76 m farther than the jogger</u>
