Final answer:
The estimated distance traveled over the interval [0, 3] is 46.5 meters using the trapezoidal rule with the given velocity-time data.
Step-by-step explanation:
To estimate the distance traveled over the interval [0, 3], you can use the trapezoidal rule to approximate the area under the velocity-time graph. The formula for this approximation is:
Distance=Δt( v_0 +v_1 / 2 + v_1 +v_2 / 2 +…+ v_n−1 +v_n / 2 )
where Δt is the time interval and v_i is the velocity at time t_i .
Given your data, we have
Δt=0.5 seconds, and the velocities are:
v_0 =0,v_1 =12,v_2 =16,v_3 =25,v_4 =20,v_5 =12, v_6 =16
Now, plug these values into the formula:
Distance=0.5( 0+12 / 2 + 12+16/ 2 + 16+25 /2 + 25+20 /2 + 20+12 / 2 + 12+16 / 2 )
Distance=0.5(6+14+20.5+22.5+16+14)
Distance=0.5×93
Distance=46.5meters
So, the estimated distance traveled over the interval [0, 3] is 46.5 meters.
Your complete question is: Compute R6, L6, and M3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows.
time t(s) 0 0.5 1 1.5 2 2.5 3
velocity v(m/s) 0 12 16 25 20 12 16