The velocity of a car is f(t)=7t meters/second. Use a graph of f(t) to find the exact distance traveled by the car, in meters, from t = 0 to t = 10 seconds
draw the curve. THe area under the curve from t=0 to t=7 is distance (velocity*time=distance).
It should be a triangle, and you can figure the area of that.
The easier way is to use integral calculus:
distance= INT (f(t))dt=INT 7t*dt from 0 to 7 = 7/2 49
check that with your graph.
Does it mean, 0.5*10*70=350 m?
To find the exact distance traveled by the car, we need to integrate the velocity function over the given time interval.
The velocity function is given as f(t) = 7t meters/second.
To integrate f(t) with respect to t, we use the integral calculus notation:
∫ f(t) dt.
In this case, we integrate f(t) = 7t with respect to t from t = 0 to t = 10 seconds:
∫[0 to 10] 7t dt.
Evaluating this integral gives us the distance traveled by the car:
∫[0 to 10] 7t dt = 3.5t^2 |[0 to 10].
Evaluating this expression with the limits of integration, we get:
= 3.5(10)^2 - 3.5(0)^2
= 3.5(100) - 3.5(0)
= 350 - 0
= 350 meters.
Therefore, the exact distance traveled by the car from t = 0 to t = 10 seconds is 350 meters.