Question

A motorist travelling at $54km/hr$ when he observes a traffic signal at a distance of $280m$ ahead turning red at time $t=0$. If he decides to decelerate & then accelerates by the same magnitude, so as to pass the signal at $54km/hr$ at $t=28$ seconds, when the signal turns green, then

• A. Magnitude of deceleration is $\frac{5}{7}m/s^2$
• B. Magnitude of deceleration is $1m/s^2$
• C. Minimum speed reached is $5m/s$
• D. Minimum speed reached is $10m/s$

Answer 1

Answer: (D)

Minimum speed reached is $10m/s$

$u=54km/hr=54\times \frac{1000}{3600}m/s$

$u=15m/s$

Now, from $A$ to $B$

$S=ut+\frac{1}{2}a{t}^2$

$140=15\times 14-\frac{1}{2}a\times (14{)}^2$

$a=\frac{70}{98}m/s^2=\frac{5}{7}m/s^2$

$V_B=u-at$

$V=15-\frac{5}{7}\times 14=10m/s$.