Question

What is the train's acceleration if it has a uniform acceleration which travels 10m in one second and 32m in the next two seconds (the book's answer says 4 for some reason)?

Answer 1

To determine the acceleration of the train, we can use the equation for uniformly accelerated motion:

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

where:

• d is the displacement
• u is the initial velocity
• t is the time
• a is the acceleration

Let's analyze the given information step by step:

1. In the first second, the train travels a distance of 10m. Let's assume the initial velocity is u1, and the time taken is t1 = 1 second.

   Therefore, we have: $d=10$m $u=u1$ $t=t1=1$s

   Plugging these values into the equation, we get: $10=u1+\frac{1}{2}a(1{)}^2$

   Simplifying the equation, we have: $10=u1+\frac{1}{2}a$

   Equation 1: u1+12a=10u1 + frac{1}{2}a = 10u1+21​<span clas