Question

a racing car accelerates uniformly from rest along a straight track. this track has markers spaced at equal distances along it from the start, as shown in the figure. the car reaches a speed of 140 km/h as it passes marker 2. where on the track was the car when it was traveling at 70 km/h?

Answer 1

The point where the car was traveling at 70 km/h is at 1/4 of the distance from marker 2 back towards the start because the distance is proportional to the square of the time in uniform acceleration.

Step-by-step explanation:

The student's question relates to the topic of uniform acceleration in Physics. As the racing car accelerates uniformly from rest and reaches a speed of 140 km/h upon passing marker 2, we need to find the point on the track where the car was traveling at 70 km/h. Since the acceleration is uniform, we can use the fact that the distance travelled under uniform acceleration is proportional to the square of the time. If it takes t seconds to reach 140 km/h, it will take t/2 seconds to reach 70 km/h, which is half the final speed. Thus, the distance travelled to reach 70 km/h will be (1/2)^2 = 1/4 of the total distance travelled to reach 140 km/h. Therefore, the car was at 1/4 of the distance from marker 2 towards the start when it was traveling at 70 km/h.

Answer 2

To determine where the car was when it was traveling at 70 km/h, we can use the equation of motion relating acceleration, velocity, and distance.

Step-by-step explanation:

To determine where the car was when it was traveling at 70 km/h, we can use the equation of motion relating acceleration, velocity, and distance. Since the car accelerates uniformly, the equation is:

v^2 = u^2 + 2as

where v is the final velocity (70 km/h), u is the initial velocity (0 km/h), a is the acceleration, and s is the distance. We know that the car reached a speed of 140 km/h when it passed marker 2, so we can calculate the acceleration:

140^2 = 0^2 + 2a imes 2d

Simplifying this equation, we find that a = 980/d. Using this acceleration value, we can calculate the distance the car traveled to reach a speed of 70 km/h:

70^2 = 0^2 + 2a imes s

Substituting the acceleration value, we get 490 = 0 + 980/d imes s. Solving for s, we find that s = d/2. Therefore, the car was halfway between markers 1 and 2 when it was traveling at 70 km/h.