Physics Question

Question

During the first 25 minutes of a 3.0 hr trip, a car has an average speed 39 km/h.

What must the average speed in km/h of the car during the rest of the trip be if the car is to have an average speed of 71.0 km/h for the entire trip? Keep two decimal places.

Answer 1

Avg Speed = total distance / total time =(∑v_it_i)/∑t_i

t1 = 25/60 =5/12hr, v1 = 39kmph,

t2 = 3-5/12 = 31/12 hr, v2 =?

vavg = 71.0 kmph

Plugging in the values 71 = (39*5/12 + v2 * 31/12)/3

or v2 = (3 *71 - 39*5/12) /(31/12) = (3*12*71 - 39*5)/31 = 76.16

The average speed of the car for the rest of the trip is 76.16 kmph

Answer 2

Remember the formula: average velocity = total distance/total time

Let's break this problem into parts:

This car traveled this trip at two different speeds

(1) 39 km/h for 25 minutes

(2) ? km/h for rest of 3 hrs, or 2 hr 35 min

Total: 71 km/h average for 3 hrs

To find the average speed, we take the total distance divided by time. We know the average speed and total time the entire trip took, so this will help us find the total distance traveled.

71 km/h * 3 h = 213 km

We can find the average speed of the second part of the trip if we know the distance traveled during that part of the trip. We can find this particular piece of information if we know both the total distance traveled and the distance traveled during the first part of the trip.

The total distance covered is distance = average velocity * time = 39 km/h * 25 min * 1 h/60 min = 16.25 km. Notice we had to convert the units of time to hours to cancel out with km/h.

The distance traveled in the second part of the trip is 213 km - 16.25 km = 196.75 km.

With the time -- 2 hr 35 min, we can calculate the average velocity during the second part of the trip.

Converting 2 hr 35 min into hours is the same as 2 hr + 35min/60min = 2 7/12 hr.

The average velocity during the second part of the trip = distance/time = 196.75 km/ (2 7/12 h) = 76.16 km/h.

Therefore, the average speed in km/h of the car during the rest of the trip is 76.16 km/h.