df <- data.frame(time = c(10,20,30,50,100,200,500,1000),
                    A = c(1.5,2.5,2.8,4.5,5.4,6.2,7.4,8.1),
                    B = c(1.6,2.6,2.7,4.4,4.9,6.1,7.5,8),
                    C = c(1.4,2.4,2.6,4.2,4.9,5.9,7.8,7.9))

melted_df <- data.table::melt(df, id.vars = c("time"), variable.name = c("group"))

av <- aov(value~group+time+group:time, data = melted_df)
 av

        Df Sum Sq Mean Sq F value   Pr(>F)
 group        2   0.11    0.05   0.025    0.975
 time         1  83.26   83.26  39.506 6.32e-06 ***
 group:time   2   0.02    0.01   0.005    0.995
 Residuals   18  37.93    2.11
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1