Question

A car moves in a straight line at 16.0 m/s for 8.0 miles, then at 30.0 m/s for another 8.0 miles.
(a)
Is the car's average speed less than, greater than, or equal to 23.0 m/s?
less than 23.0 m/s
equal to 23.0 m/s
greater than 23.0 m/s
(b)
Calculate the car's average speed in meters/second. (Enter your answer to three significant figures.)

_____m/s

Answer 1

Answer:

a)The car's average speed less than 23.0 m/s.

b) The car's average speed is 20.9 m/s.

Explanation:

a) A car moves in a straight line at 16.0 m/s for 8.0 miles.

Distance covered = $d_1=8.0 miles =12874.72 m$

1 mile = 1609.34 m

Time taken by the car to cover 8 mile distance = $t_1$

Speed of the car = $S_1=16.0 m/s$

$S_1=\frac{d_1}{t_1}$

$16.0 m/s=\frac{12874.72 m}{t_1}$

$t_1=\frac{12874.72 m}{16.0 m/s}=804.67 s$

After this car moves in a straight line at 30.0 m/s for 8.0 miles.

Distance covered = $d_2=8.0 miles =12874.72 m$

Time taken by the car to cover further 8 mile distance = $t_2$

Speed of the car = $S_2=30.0 m/s$

$S_2=\frac{d_2}{t_2}$

$30.0 m/s=\frac{12874.72 m}{t_2}$

$t_2=\frac{12874.72 m}{30.0 m/s}=429.16 s$

Average speed = $\frac{d_1+d_2}{t_1+t_2}$

=$\frac{12874.72 m+12874.72 m}{804.67 s+429.16 s}=20.87 m/s$

Average speed of the car is 20.87 m/s which is less than 23.0 m/s speed.

b)The car's average speed =  20.87 m/s ≈ 20.9 m/s

Answer 2

(a)  The car's average speed is less than 23 m/s

(b)  The average speed of the car is 20.87 m/s

The given parameters;

• initial speed of the car, u = 16 m/s

• final speed of the car, v = 30 m/s

• distance traveled, d = 8 miles = 12874.8 meters

(b) The average speed of the car is calculated as;

$t_1 = \frac{12874.8}{16} = 804.68 \ s\\\\t_2 = \frac{12874.8}{30} = 429.16 \ s\\\\V_{avg.} = \frac{Total \ distance }{Total \ time} = \frac{2(12874.8)}{804.68 + 429.16} = 20.87 \ m/s$

The average speed of the car is 20.87 m/s

(a) Thus, we can conclude that the car's average speed is less than 23 m/s

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