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
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?
5 answers
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
A. 12
B. 13.3
C. 40
D. 48
E. 37
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
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
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
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
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