Answer:
15.8640053791 s
392.780107582 m
29.5184032275 m/s
Explanation:
0 denotes initial
x denotes displacement
c denotes car
t denotes truck
r denotes rear
[tex]x_0_{cr}=-49.5\ m[/tex]
[tex]a_c=0.6\ m/s^2[/tex]
[tex]x_0_{t}=0[/tex]
[tex]v_0_{c}=v_0_{t}[/tex]
For the car
[tex]x_c=x_0+v_0_{c}t+\dfrac{1}{2}at^2[/tex]
The displacement of the truck will be
[tex]x_t=v_tt[/tex]
From the above two equations we get
[tex]x_c-x_t=x_0+v_0_{c}+\dfrac{1}{2}at-v_{t}t=26\\\Rightarrow 26=x_0+\dfrac{1}{2}at^2\\\Rightarrow 26+49.5=\dfrac{1}{2}0.6t^2\\\Rightarrow t=\sqrt{\dfrac{2(26+49.5)}{0.6}}\\\Rightarrow t=15.8640053791\ s[/tex]
The time taken is 15.8640053791 s
[tex]x-x_0=v_{0}_{c}t+\dfrac{1}{2}at^2\\\Rightarrow x-x_0=20\times 15.8640053791+\dfrac{1}{2}0.6\times 15.8640053791^2\\\Rightarrow x-x_0=392.780107582\ m[/tex]
The distance the car travels is 392.780107582 m
[tex]v=v_0+at\\\Rightarrow v=20+0.6\times 15.8640053791\\\Rightarrow v=29.5184032275\ m/s[/tex]
The velocity of the car is 29.5184032275 m/s
