14. A racing car accelerates uniformly through three gears, changes with the following average speed:
20 for 2.0 s
40 for 2.0 s
60 for 6.0 s
What is the overall average speed of the car?
Using the definition of the average speed v (ave) = total distance/ time taken, we obtaine
d1 = v1•t1= 20•2 = 40 m
d2 = v2•t2 = 40•2 = 80 m
d3= v3•t3 = 60•6 =360 m
d= d1+d2+d3 = 40 + 80+360 =480 m
t= t1+t2+t3 = 2+2+6 = 10 s
v(ave) = d/t =480/140 =48 m/s
according to def v=d/t
d1 = v1•t1= 20•2 = 40 m
d2 = v2•t2 = 40•2 = 80 m
d3= v3•t3 = 60•6 =360 m
d= d1+d2+d3 = 40 + 80+360 =480 m
t= t1+t2+t3 = 2+2+6 = 10 s
v(ave) = d/t =480/140 =48 m/s
To find the overall average speed of the car, we need to calculate the total distance traveled and divide it by the total time taken.
First, let's calculate the distance traveled in each gear:
In the first gear, the car travels at an average speed of 20 m/s for 2.0 seconds. Therefore, the distance traveled in the first gear can be calculated as:
Distance1 = Average speed1 * Time1
Distance1 = 20 m/s * 2.0 s
Distance1 = 40 meters
In the second gear, the car travels at an average speed of 40 m/s for 2.0 seconds. Therefore, the distance traveled in the second gear can be calculated as:
Distance2 = Average speed2 * Time2
Distance2 = 40 m/s * 2.0 s
Distance2 = 80 meters
In the third gear, the car travels at an average speed of 60 m/s for 6.0 seconds. Therefore, the distance traveled in the third gear can be calculated as:
Distance3= Average speed3 * Time3
Distance3 = 60 m/s * 6.0 s
Distance3 = 360 meters
Now, let's calculate the total distance traveled by adding up the distances in each gear:
Total Distance = Distance1 + Distance2 + Distance3
Total Distance = 40 meters + 80 meters + 360 meters
Total Distance = 480 meters
Next, we need to calculate the total time taken by adding up the times in each gear:
Total Time = Time1 + Time2 + Time3
Total Time = 2.0 s + 2.0 s + 6.0 s
Total Time = 10.0 seconds
Finally, we can calculate the overall average speed of the car by dividing the total distance traveled by the total time taken:
Overall Average Speed = Total Distance / Total Time
Overall Average Speed = 480 meters / 10.0 seconds
Overall Average Speed = 48 meters per second
Therefore, the overall average speed of the car is 48 meters per second.
Sir Steve I got the ans 46 but the correct ans is 48
S=vt+1/2at^2
in 1st gear
S=v*2+1/2*20*2^2
S=2v+40..........eq 1
in second gear
S=vt+1/2at^2
s=v*2+1/2*40*2^2
S=v+80.........eq 2
in third gear
S=vt+1/2at^2
S=v*6=1/2*60*6^2
S=6v+1080.......eq 3
substituting eq 3 in eq 2 we get
6v+1080=2v+80
6v-2v=80-1080
4v=-1000
v=-250
substituting the value of v in eq 1 we get
s=2v+40
s=2*-250+40
s=-460
vav=d/t
vav=460/10=46ms^-1
Sir but the and which u got is the same as i got but its not given in the options. here are the options
A. 12
B. 13.3
C. 40
D. 48
E. 37
average speed is distance / time
with initial velocity v, the distance s after time t is
s = vt + 1/2 at^2
and speed is v + at
at a=20, s = 0 + 1/2 * 20 * 2^2 = 40, v=20*2 = 40
at a=40, s = 40*2 + 1/2 * 40 * 2^2 = 160, v = 40+40*2 = 120
at a=60,
s = 120*6 + 1/2 * 60 * 6^2 = 1800
total distance: 40+120+1800 = 1960
total time: 2+2+6 = 10
avg speed: 1960/10 = 196