Question

Two cars on a straight road at time zero are beside each other. The first car, traveling at speed 30 m/s, is passing the second car, which is traveling at 24 m/s. Seeing a cow on the road ahead, the driver of each car starts to slow down at

6.0 m/s 2
. Find the expression of the position of the first car. Assume it to be zero initially.

(t)=30t− 1/26t

Answer 1

The expression for the position of the first car is x1(t) = 30t - 1/26t².

Step-by-step explanation:

To find the expression for the position of the first car, we can start by considering the motion of each car individually. The first car is traveling at a speed of 30 m/s and starts to slow down at a rate of 6.0 m/s². We can use the equation for position with constant acceleration to find its expression: x1(t) = xo1 + vo1t + 1/2at². Since the initial position (xo1) is given as zero, the expression simplifies to: x1(t) = vo1t + 1/2at².

Substituting the given values, vo1 = 30 m/s and a = -6.0 m/s², the expression for the position of the first car can be written as: x1(t) = 30t - 1/26t².