Answer:
The right answer is "1.369 m/s²".
Explanation:
The given values are:
Distance (s)
= 260 m
Initial speed (u)
= 26 m/s
Reaction time (t')
= 0.51 s
During reaction time, the distance travelled by locomotive will be:
⇒ [tex]s'=ut'[/tex]
[tex]=26\times 0.51[/tex]
[tex]=13.26 \ m[/tex]
Remained distance between locomotive and car:
⇒ [tex]x=s-s'[/tex]
[tex]=260-13.26[/tex]
[tex]=246.74 \ m[/tex]
Now,
The final velocity to avoid collection is, V = 0 m/s
From third equation of motion:
⇒ [tex]V^2=u^2+2ax[/tex]
On putting the estimated values, we get
⇒ [tex]0=(26)^2+2\times a\times 246.74[/tex]
⇒ [tex]0=676+493.48a[/tex]
⇒ [tex]493.48a=-676[/tex]
⇒ [tex]a=-\frac{676}{493.48}[/tex]
⇒ [tex]a=1.369 \ m/s^2[/tex]