A bicycle moves with a constant velocity of 5 km/h for 10 minutes and then decelerates at the rate 1 km/h^2, till it stops. Find the total distance covered by the bicycle
Answers
Answer:
13333 m, or 13km.
.
Explanation:
let me rephrase the question to avoid confusion:
A bicycle moves in a straight line with a constant velocity of
5
k
m
h
for 10 mins and then decelerates at the rate of
1
k
m
h
2
till it stops. Find the total distance covered by the bicycle.
First, to find the distance covered at the first 10 mins, we multiply the bicycle's speed by the time
5
k
m
h
⋅
10
60
h
=
5
6
k
m
Now we need to find the distance travelled after it starts to decelerate. This is how the speed as a function of time looks like from the moment the bicycle starts to decelerate. (ignore the negative part)
the x-axis represents the time in hours.
the y-axis represents the speed of bicycle in km/hour
graph{y=5-x [-10, 10, -5, 5]}
as shown above, the speed goes from 5km/hour goes down to 0 as time passes.
the distance covered is actually the area of the triangle formed by the diagonal line cutting across the x-axis and y-axis.
Thus the distance traveled here is the surface area of the triangle:
5
k
m
h
⋅
5
h
2
=
12.5km#
now the total distance is:
5
6
k
m
+
12.5
k
m
=
13
1
3
k
m
=
13333
1
3
m
≈
13333
m
≈
13
k
m